Finite-dimensional approximation of the inverse frame operator |
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Authors: | Ole Christensen |
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Institution: | (1) Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark |
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Abstract: | A frame in a Hilbert space
allows every element in
to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of
those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually
it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce
a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate
the frame coefficients (even inl
2) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg
frames and wavelet frames. |
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Keywords: | 42C15 41A35 |
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